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Simplifying (x + -3)(x + -3)(x + 2 + -3i)(x + 2 + 3i) = 0 Reorder the terms: (-3 + x)(x + -3)(x + 2 + -3i)(x + 2 + 3i) = 0 Reorder the terms: (-3 + x)(-3 + x)(x + 2 + -3i)(x + 2 + 3i) = 0 Reorder the terms: (-3 + x)(-3 + x)(2 + -3i + x)(x + 2 + 3i) = 0 Reorder the terms: (-3 + x)(-3 + x)(2 + -3i + x)(2 + 3i + x) = 0 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x))(2 + -3i + x)(2 + 3i + x) = 0 ((-3 * -3 + x * -3) + x(-3 + x))(2 + -3i + x)(2 + 3i + x) = 0 ((9 + -3x) + x(-3 + x))(2 + -3i + x)(2 + 3i + x) = 0 (9 + -3x + (-3 * x + x * x))(2 + -3i + x)(2 + 3i + x) = 0 (9 + -3x + (-3x + x2))(2 + -3i + x)(2 + 3i + x) = 0 Combine like terms: -3x + -3x = -6x (9 + -6x + x2)(2 + -3i + x)(2 + 3i + x) = 0 Multiply (9 + -6x + x2) * (2 + -3i + x) (9(2 + -3i + x) + -6x * (2 + -3i + x) + x2(2 + -3i + x))(2 + 3i + x) = 0 ((2 * 9 + -3i * 9 + x * 9) + -6x * (2 + -3i + x) + x2(2 + -3i + x))(2 + 3i + x) = 0 ((18 + -27i + 9x) + -6x * (2 + -3i + x) + x2(2 + -3i + x))(2 + 3i + x) = 0 (18 + -27i + 9x + (2 * -6x + -3i * -6x + x * -6x) + x2(2 + -3i + x))(2 + 3i + x) = 0 Reorder the terms: (18 + -27i + 9x + (18ix + -12x + -6x2) + x2(2 + -3i + x))(2 + 3i + x) = 0 (18 + -27i + 9x + (18ix + -12x + -6x2) + x2(2 + -3i + x))(2 + 3i + x) = 0 (18 + -27i + 9x + 18ix + -12x + -6x2 + (2 * x2 + -3i * x2 + x * x2))(2 + 3i + x) = 0 Reorder the terms: (18 + -27i + 9x + 18ix + -12x + -6x2 + (-3ix2 + 2x2 + x3))(2 + 3i + x) = 0 (18 + -27i + 9x + 18ix + -12x + -6x2 + (-3ix2 + 2x2 + x3))(2 + 3i + x) = 0 Reorder the terms: (18 + -27i + 18ix + -3ix2 + 9x + -12x + -6x2 + 2x2 + x3)(2 + 3i + x) = 0 Combine like terms: 9x + -12x = -3x (18 + -27i + 18ix + -3ix2 + -3x + -6x2 + 2x2 + x3)(2 + 3i + x) = 0 Combine like terms: -6x2 + 2x2 = -4x2 (18 + -27i + 18ix + -3ix2 + -3x + -4x2 + x3)(2 + 3i + x) = 0 Multiply (18 + -27i + 18ix + -3ix2 + -3x + -4x2 + x3) * (2 + 3i + x) (18(2 + 3i + x) + -27i * (2 + 3i + x) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 ((2 * 18 + 3i * 18 + x * 18) + -27i * (2 + 3i + x) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 ((36 + 54i + 18x) + -27i * (2 + 3i + x) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + (2 * -27i + 3i * -27i + x * -27i) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 Reorder the terms: (36 + 54i + 18x + (-54i + -27ix + -81i2) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + (-54i + -27ix + -81i2) + 18ix * (2 + 3i + x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + (2 * 18ix + 3i * 18ix + x * 18ix) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 Reorder the terms: (36 + 54i + 18x + -54i + -27ix + -81i2 + (36ix + 18ix2 + 54i2x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + (36ix + 18ix2 + 54i2x) + -3ix2 * (2 + 3i + x) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + (2 * -3ix2 + 3i * -3ix2 + x * -3ix2) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 Reorder the terms: (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + (-6ix2 + -3ix3 + -9i2x2) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + (-6ix2 + -3ix3 + -9i2x2) + -3x * (2 + 3i + x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + (2 * -3x + 3i * -3x + x * -3x) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 Reorder the terms: (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + (-9ix + -6x + -3x2) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + (-9ix + -6x + -3x2) + -4x2 * (2 + 3i + x) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + (2 * -4x2 + 3i * -4x2 + x * -4x2) + x3(2 + 3i + x)) = 0 Reorder the terms: (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + (-12ix2 + -8x2 + -4x3) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + (-12ix2 + -8x2 + -4x3) + x3(2 + 3i + x)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + -12ix2 + -8x2 + -4x3 + (2 * x3 + 3i * x3 + x * x3)) = 0 Reorder the terms: (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + -12ix2 + -8x2 + -4x3 + (3ix3 + 2x3 + x4)) = 0 (36 + 54i + 18x + -54i + -27ix + -81i2 + 36ix + 18ix2 + 54i2x + -6ix2 + -3ix3 + -9i2x2 + -9ix + -6x + -3x2 + -12ix2 + -8x2 + -4x3 + (3ix3 + 2x3 + x4)) = 0 Reorder the terms: (36 + 54i + -54i + -27ix + 36ix + -9ix + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: 54i + -54i = 0 (36 + 0 + -27ix + 36ix + -9ix + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 (36 + -27ix + 36ix + -9ix + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: -27ix + 36ix = 9ix (36 + 9ix + -9ix + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: 9ix + -9ix = 0 (36 + 0 + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 (36 + 18ix2 + -6ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: 18ix2 + -6ix2 = 12ix2 (36 + 12ix2 + -12ix2 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: 12ix2 + -12ix2 = 0 (36 + 0 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 (36 + -3ix3 + 3ix3 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: -3ix3 + 3ix3 = 0 (36 + 0 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 (36 + -81i2 + 54i2x + -9i2x2 + 18x + -6x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: 18x + -6x = 12x (36 + -81i2 + 54i2x + -9i2x2 + 12x + -3x2 + -8x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: -3x2 + -8x2 = -11x2 (36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -4x3 + 2x3 + x4) = 0 Combine like terms: -4x3 + 2x3 = -2x3 (36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4) = 0 Solving 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + -36 + x4 = 0 + -36 Reorder the terms: 36 + -36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + -36 -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + -36 Combine like terms: 0 + -36 = -36 -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = -36 Add '-12x' to each side of the equation. -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + -12x + x4 = -36 + -12x Reorder the terms: -81i2 + 54i2x + -9i2x2 + 12x + -12x + -11x2 + -2x3 + x4 = -36 + -12x Combine like terms: 12x + -12x = 0 -81i2 + 54i2x + -9i2x2 + 0 + -11x2 + -2x3 + x4 = -36 + -12x -81i2 + 54i2x + -9i2x2 + -11x2 + -2x3 + x4 = -36 + -12x Add '11x2' to each side of the equation. -81i2 + 54i2x + -9i2x2 + -11x2 + -2x3 + 11x2 + x4 = -36 + -12x + 11x2 Reorder the terms: -81i2 + 54i2x + -9i2x2 + -11x2 + 11x2 + -2x3 + x4 = -36 + -12x + 11x2 Combine like terms: -11x2 + 11x2 = 0 -81i2 + 54i2x + -9i2x2 + 0 + -2x3 + x4 = -36 + -12x + 11x2 -81i2 + 54i2x + -9i2x2 + -2x3 + x4 = -36 + -12x + 11x2 Add '2x3' to each side of the equation. -81i2 + 54i2x + -9i2x2 + -2x3 + 2x3 + x4 = -36 + -12x + 11x2 + 2x3 Combine like terms: -2x3 + 2x3 = 0 -81i2 + 54i2x + -9i2x2 + 0 + x4 = -36 + -12x + 11x2 + 2x3 -81i2 + 54i2x + -9i2x2 + x4 = -36 + -12x + 11x2 + 2x3 Add '-1x4' to each side of the equation. -81i2 + 54i2x + -9i2x2 + x4 + -1x4 = -36 + -12x + 11x2 + 2x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -81i2 + 54i2x + -9i2x2 + 0 = -36 + -12x + 11x2 + 2x3 + -1x4 -81i2 + 54i2x + -9i2x2 = -36 + -12x + 11x2 + 2x3 + -1x4 Reorder the terms: 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = -36 + -12x + 11x2 + 2x3 + -1x4 + 36 + 12x + -11x2 + -2x3 + x4 Reorder the terms: 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = -36 + 36 + -12x + 12x + 11x2 + -11x2 + 2x3 + -2x3 + -1x4 + x4 Combine like terms: -36 + 36 = 0 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + -12x + 12x + 11x2 + -11x2 + 2x3 + -2x3 + -1x4 + x4 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = -12x + 12x + 11x2 + -11x2 + 2x3 + -2x3 + -1x4 + x4 Combine like terms: -12x + 12x = 0 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + 11x2 + -11x2 + 2x3 + -2x3 + -1x4 + x4 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 11x2 + -11x2 + 2x3 + -2x3 + -1x4 + x4 Combine like terms: 11x2 + -11x2 = 0 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4 Combine like terms: 2x3 + -2x3 = 0 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 + -1x4 + x4 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 36 + -81i2 + 54i2x + -9i2x2 + 12x + -11x2 + -2x3 + x4 = 0 The solution to this equation could not be determined.
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